Reports have surfaced that some Snow Leopard users are finding themselves unable to send messages from within Apple Mail, though they continue to receive messages. Upon attempting to send mail, many users receive an alert message that states, "Error 54: Connection Reset By Peer." Yet, not all users receive an error message; some simply see their message fail to send. Apple recently acknowledged this issue in a, and suggested a couple of workarounds.
In the article, Apple explains that Mail in Snow Leopard (as opposed to Leopard) sends messages through a different port rotation for the "Default ports" setting, and thus some users may need to update their SMTP authentication settings for outgoing messages. The article goes on to provide information regarding how to do so, and, should this first option fail, how to change the port that Mail sends through.
However, back-and-forth on Apple's discussion forums indicate that Apple's suggestions aren't working for everyone. In a, some users have reported that calls to Apple indicate engineers are in the process of developing an update to resolve the issue - though Apple has not officially confirmed this. Such an update would likely ship with the 10.6.1 update, which, if past performance is any indication, should be available within a week or so.
Until more is known about this issue, there isn't much affected users can do beyond trying what Apple suggests other than switching temporarily to another email client for sending mail. That would be a terrible workaround unless you're using IMAP, at which point you could receive incoming message with Mail, wait until they were all filtered appropriately, and then read and respond in the other program.